1. Chapter 3-1 Relations and Ordered Pairs Alg. 2 Notes

2. Cartesian Product A x B means: The product (x) of sets A and B is the set of all ordered pairs having the 1 st member from set A and the 2 nd from set B.

3. Example 1: Find the Cartesian product Q x Q, where Q = {2,3,4} Answer: {(2,2), (2,3), (2,4),(3,2), (3,3), (3,4),(4,2), (4,3), (4,4)} Notice a 3 x 3 Set has 9 elements!!

4. Example 2 Find the cartesian product A x B where set A = {stinky, farty} B = {Carl, James, Cody} Answer: {(stinky,Carl),(stinky, James), (stinky, Cody) (farty,Carl), (farty,James), (farty, Cody)} Notice: a 2 x 3 product has 6 elements!!

5. Domain and Range Domain (x) = the set of all the first members Range (y) = the set of all the second members

6. Example 3 List the domain and range of the relation {(a,1), (b,2), (c,3), (e,2)} Answer: Domain: {a,b,c,e} Range: {1,2,3,} Notice repeated elements not listed twice When you list individual elements it is called roster notation

7. Set Builder Notation: {x I x  3} read as “the set of all x such that x is less than or equal to 3” Example 4: Use the set {1,2,3,…,10} to find {x I 4 < x < 7} Answer: {5,6}

8. Example 5 Let Q = {2,3,4} (Ex 1) Use Q x Q to find {(x,y) x < y} (read: Use the cartesian product of Q to find members such that the x-value is less than the y-value. Answer: {(2,3), (2,4), (3,4)}

9. Example 6: You Try Use the relation R x R where R = {1,3,5,7}. Find {(x,y) I y = x + 2}